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The resistance of a wire is $R$. It is bent at the middle by $180^{\circ}$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is
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Verified Answer
The correct answer is:
$R / 4$
$R / 4$
Resistance of wire $(R)=\rho \frac{l}{A}$ If wire is bent in the middle then
$$
\begin{aligned}
& l^{\prime}=\frac{l}{2}, A^{\prime}=2 \mathrm{~A} \\
& \therefore \text { New resistance, } \mathrm{R}^{\prime}=\rho \frac{l^{\prime}}{\mathrm{A}^{\prime}} \\
& =\frac{\rho \frac{l}{2}}{2 A}=\frac{\rho l}{4 A}=\frac{R}{4} \text {. } \\
&
\end{aligned}
$$
$$
\begin{aligned}
& l^{\prime}=\frac{l}{2}, A^{\prime}=2 \mathrm{~A} \\
& \therefore \text { New resistance, } \mathrm{R}^{\prime}=\rho \frac{l^{\prime}}{\mathrm{A}^{\prime}} \\
& =\frac{\rho \frac{l}{2}}{2 A}=\frac{\rho l}{4 A}=\frac{R}{4} \text {. } \\
&
\end{aligned}
$$
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